The limit of a function of two variables along a path
Here, we consider the value of as . A common way to do this is to imagine the point approaching along a path. Often, the path is a straight line, but other paths are possible, too. As the point approaches , we see what value is approaching. If different paths cause to approach different limits, then we know that the limit of of as does not exist.
In the figure, select an example and select a path. Then, click and drag the graph to rotate it and see the -values along the path.
Developed for use with Thomas' Calculus, published by Pearson.